<abstract xmlns="http://www.w3.org/1999/xhtml">
Let <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_amsil-2023-0016_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>P</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></msubsup><mrow><msub><mrow><mi>a</mi></mrow><mi>j</mi></msub><msup><mrow><mi>z</mi></mrow><mi>j</mi></msup></mrow></mrow></math>
<tex-math>P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}}</tex-math>
</alternatives>
</inline-formula> be a polynomial of degree <italic>n </italic>such that <italic>a</italic><italic>n </italic> ≥ <italic>a</italic><italic>n−</italic>1 ≥ . . . ≥ <italic>a</italic>1 ≥ <italic>a</italic>0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of <italic>P </italic>(<italic>z</italic>) lie in <italic>|z| ≤ </italic>1. This result has been generalized in various ways (see [1, 3, 4, 6, 7]). In this paper we shall prove some generalizations of the results due to Aziz and Zargar [1, 2] and Nwaeze [7].
</abstract>

Let 


P(z)=∑j=0najzj
P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}}

 be a polynomial of degree n such that an  ≥ an−1 ≥ . . . ≥ a1 ≥ a0 ≥ 0. Then according to Eneström-Kakeya theorem all the zeros of P (z) lie in |z| ≤ 1. This result has been generalized in various ways (see [1, 3, 4, 6, 7]). In this paper we shall prove some generalizations of the results due to Aziz and Zargar [1, 2] and Nwaeze [7].

On the Zeros of Polynomials with Restricted Coefficients

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"On the Zeros of Polynomials with Restricted Coefficients"}

Let 


P(z)=∑j=0najzj
P\left( z \right) = \sum\nolimits_{j = 0}^n {{a_j}{z^j}}

 be a polynomial of degree n such that an  ≥ an−1 ≥ . . . ≥ a1 ≥ a0 ≥ 0. Then...

On the Zeros of Polynomials with Restricted Coefficients

Pubblicato online: 13 set 2023

Pagine: 306 - 314

Ricevuto: 21 gen 2023

Accettato: 17 ago 2023

DOI: https://doi.org/10.2478/amsil-2023-0016

Parole chiave
polynomial, zeros, restricted coefficients

© 2023 B. A. Zargar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On the Zeros of Polynomials with Restricted Coefficients

Pubblicato online: 13 set 2023

Pagine: 306 - 314

Ricevuto: 21 gen 2023

Accettato: 17 ago 2023

DOI: https://doi.org/10.2478/amsil-2023-0016

Parole chiavepolynomial, zeros, restricted coefficients

© 2023 B. A. Zargar et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Parole chiave
polynomial, zeros, restricted coefficients